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188 Multibody Systems Approach to Vehicle Dynamics
in a force element that represents the behaviour of the tyre. The force element
acts between the centre of the wheel and a point on the jack coincident
with the centre of the tyre contact patch. In this case this is assumed to be
directly below the wheel centre. It is important that the force element for
the tyre acts only in compression and allows the tyre to lift off the top of the
jack if the input is severe enough.
The tyre is taken to have linear radial stiffness of 160 N/mm and a damping
coefficient of 0.5 Ns/mm. The undeformed radius of the tyre, equivalent to
the free length of the tyre spring, is taken here to be 318 mm. A step function
can also be used to zero the tyre force if contact with the jack is lost.
The full definition can be accomplished using the following SFORCE
statement that is taken to act between Marker 1010 at the wheel centre and
Marker 2029 on the jack part:
SFORCE/1029, I1010, J2029, TRANS
,FUSTEP(318DM(1010,2029),0,0,0.1,160*(318DM(1010,2029))
0.5*VR(1010,2029))
The next step is to define the motion imparted to the jack part to represent the
input from the road surface. This is illustrated in Figure 4.52 where the profile
for a ‘sleeping policeman’ road obstacle is given. The profile is defined as
a set of xy pairs. Note here that the xy values are local to the definition of the
obstacle profile and not associated with the X- and Y-axes of the ground reference
frame. The vehicle is assumed to be moving with a forward speed of
10 m/s so that the x values associated with distance can be converted to time.
10 m/s
Z
X
GRF
1000 200 200 200 200 200 200 10 000
y
x
1
2
3
4
5 6
100
7
8 9
Point
1
2 3 4 5 6 7 8 9
Distance x (mm)
Time x (s)
Height y (mm)
0 1000 1200 1400 1600 1800 2000 2200 12 200
0 0.10 0.12 0.14 0.16 0.18 0.20 0.22 1.22
0 0 50 100 100 100 50 0 0
Fig. 4.52
Road profile for ‘sleeping policeman’ speed bump